The curves f(x)=x2+3x1\displaystyle {f{{\left({x}\right)}}}={x}^{{2}}+{3}{x}-{1} and g(x)=3x+15\displaystyle {g{{\left({x}\right)}}}=-{3}{x}+{15} intersect at the point (2,9).

Find the acute angle of intersection, in radians on the domain 0tπ2\displaystyle {0}\le{t}\le\frac{\pi}{{2}}, to two decimal places.